Gay rights groups that have been frustrated with a lack of action from Mr. Obama on key issues applauded the decision announced by the White House Thursday, but some activists said he can do more.

“My uncle would be so proud of this high honor,” said Stuart Milk, the honoree’s nephew, who will accept the award at the Aug. 12 White House ceremony.

“[Mr. Milk’s] election was, for him, a beginning - a chance to make real change. That change is happening, but we still have so far to go,” Mr. Milk said.

Gay Democrats have withheld fundraising from the party after the Obama Justice Department defended the Defense of Marriage Act and because he has not yet fulfilled his promise to repeal that and the Don’t Ask, Don’t Tell ban on gays serving openly in the military. He has, however, extended some benefits to same-sex partners of gay federal workers.

The honor for Mr. Milk came among the White House’s announcement of 16 medal recipients, from lesbian tennis legend Billie Jean King to close Obama friend Sen. Edward M. Kennedy, Massachusetts Democrat, and former Supreme Court Justice Sandra Day O’Connor, the first woman to sit on the high court.

Mr. Obama said his selections share “one overarching trait: Each has been an agent of change.”

“Each saw an imperfect world and set about improving it, often overcoming great obstacles along the way,” he said. “Their relentless devotion to breaking down barriers and lifting up their fellow citizens sets a standard to which we all should strive.”

The Gay & Lesbian Victory Fund said Mr. Milk’s 1977 election as the first openly gay elected official in a major U.S. city “triggered a political awakening that inspires us still today.”

“This recognition sends an important message about how critical political leadership will be in making all Americans equal in the eyes of the law,” said the group’s president, Chuck Wolfe.

Mr. Milk championed gay rights as San Francisco city supervisor; he and Mayor George Moscone were assassinated by former supervisor Dan White in November 1978.

The 2008 film “Milk” earned Sean Penn an Academy Award for Best Actor and helped to spread the activist’s story as the gay marriage battle played out in elections across the country.

Entertainment publicist Jim Strzalkowski said the honor was “too little, too late” and criticized Mr. Obama for not doing more for gay rights, such as supporting marriage equality.

He said while he doesn’t want to dismiss Mr. Milk’s record of service, Mr. Obama “can and should” do more.

“Harvey Milk is dead and there are plenty of gays suffering around the country today who need to be honored,” he said.

Gay rights groups also praised the honoring of Ms. King, one of the first openly lesbian sports players.

The White House said she has “helped champion gender equality issues not only in sports, but in all areas of public life.”

Also nominated was longtime member of Congress and 1996 Republican vice presidential nominee Jack Kemp, who died in May.